The expansion of the universe was discovered in 1929 by Edwin Hubble,
who measured the distances to a sample of nearby galaxies, and
established a correlation between distance and recession velocity.
The slope of this relation is the Hubble constant. Large systematic
uncertainties in determining distance have made an accurate
determination of the Hubble constant a challenge, and only recently
have improvements in instrumentation, the launch of the Hubble Space
Telescope (HST), and the development of several different measurement
methods led to a convergence on its value. Accurate distances to
nearby galaxies obtained as part of an HST Key Project have allowed
calibration of 5 different methods for determining the distances to
galaxies out to 500 Mpc
(Freedman
et al., 2001).
All the techniques show good agreement to within their respective
uncertainties, and yield a value

where the error bars represent
1-
statistical and systematic uncertainties, respectively (see
Figure 3). Because of the importance of its value
to so many cosmological quantities, and because of
its historically large uncertainty, H0 is often written
as H0 = 100h km sec-1 Mpc-1,
so that h = 0.72 ± 0.02 ± 0.07.

Figure 3. Hubble diagram: Low-redshift
galaxies are used to
establish the expansion of the Universe and the Hubble constant; the
consistency of the five different distance indicators is shown. The
lower panel shows the value of the Hubble constant object by object
and the convergence to 72km/s/Mpc. The scatter at distances less
than 100Mpc arises due to gravitational induced "peculiar velocities"
that arise from the inhomogeneous distribution of matter.

The largest contributions to these quoted uncertainties
result from those due to the metallicity of Cepheids, the distance to
the Large Magellanic Cloud (the fiducial nearby galaxy to which all
Cepheid distances are measured relative to), and the calibration of
the Wide Field Camera on HST. Other groups using similar techniques
(Saha et
al., 1997)
find a lower value of H0 (~ 60
km/sec/Mpc). The reasons for the difference are many, as described
further in
Freedman
et al. (2001),
but overall the determinations
are consistent to within the measurement uncertainties. Recent
measurements of H0 based on two completely independent
techniques,
the Sunyaev-Zeldovich method and the measurement of time delays for
gravitational lenses
(Reese et
al., 2000,
Keeton et
al., 2000),
are yielding values of H0 ~ 60 km/sec/Mpc with systematic errors
currently still at the 20-30% level. New results from the WMAP
satellite, discussed in the postscript to this article, give H0 =
71 ± 4 km/sec/Mpc.

Because light from very distance galaxies was emitted long ago, the
Hubble diagram also provides a means of probing the expansion at
earlier times. For many decades, efforts have been directed toward
measuring what was almost universally expected to be a slowing of the
expansion over time due to the gravity of all the matter. However,
observations by two independent groups have found that
supernovae at high redshifts are fainter than predicted for a
slowing expansion and indicate that the expansion is actually speeding
up (see Figure 4)
(Perlmutter
et al., 1999,
Riess et
al., 1998).
Although systematic effects due to intervening dust or
evolution of the supernovae themselves could explain
such a dimming of high-redshift supernovae, several tests
have failed to turn up any evidence for such effects. Apparently,
the universe is now undergoing an acceleration, with
the repulsive gravity of some strange energy form - dark energy -
at work. There is weak evidence in the supernova data for
an earlier (z > 1/2), decelerating phase
(Turner
and Riess, 2002).
Such a decelerating phase is expected on theoretical grounds (more later),
and establishing its existence (or absence!) is an important goal
of future supernova observations.

Figure 4. Hubble diagram:
High-redshift type Ia supernovae probe the expansion
history and reveal accelerated expansion. In this differential
Hubble diagram the distance modulus, which is 5 times the logarithm
of the distance, relative to an empty Universe
(0 = 0) is
plotted. Measurements from more than 200 type Ia supernova
are binned into 9 data points. The solid curves represent three
theoretical models: from the top,
=
0.7 and
M = 0.3;
=
0 and
M = 0.3;
and =
0 and
M =
1. The broken curve represents a nonaccelerating,
flat Universe (i.e., q = 0 for all z); points above this
curve indicate acceleration (adapted from data in
Tonry et
al., 2003).

The remarkable fact that the expansion is speeding up, rather
than slowing down, can be accounted for within Einstein's theory,
as the source of gravity is proportional to
( + 3p),
where the pressure p and
energy density
describe the bulk properties of
the "substance". (For ordinary or even nonbaryonic dark
matter, p = 0, while for photons
and relativistic particles, p =
/ 3.) A substance
that is very elastic, i.e., with pressure more negative
than one third its energy density, has repulsive gravity
in Einstein's theory (more later). Of course, it could well
be that the root cause of cosmic acceleration
is not new stuff (i.e., dark energy), but involves a
deeper understanding of gravity.

The deceleration parameter was introduced to quantify the slowing of
the expansion; it is related to the mass-energy content of the Universe:

(3)

where
wXpX /
X
characterizes the pressure of the
dark-energy component. (wX need not be constant; for
simplicity,
we shall assume it is.) In the absence of dark energy, a flat Universe
would decelerate by its own self-gravity (i.e., q0 =
0.5), whereas dark energy allows
for acceleration. The supernova measurements are consistent with
wX = - 1 and
X =
0.7. Independent confirmation of such a
startling result is extremely important. As discussed below, strong
indirect evidence for an additional energy component comes from a
comparison of the density of matter with measurements of
0
from fluctuations in the CMB.

Dark energy, a "mysterious substance" whose pressure is
negative and comparable in magntiude to its energy density,
apparently accounts for two-thirds of the
matter-energy budget of the universe and has no clear explanation.
Understanding its nature presents one of the greatest challenges in
both cosmology and particle physics.